[r3bl]

The goal of this is to be hosted on a router. I'm assuming it wouldn't go around NAT as much as replace NAT by replacing router's firmware.

You've guessed correctly that this is one of the most painful parts of the setup. I use a different open source product for the same purpose (Home Assistant), and it allows me to go around NAT manually (use dynamic DNS service, open up the port on a router, route it to a local device, issue a Let's Encrypt certificate) or pay them a few bucks per month to ease the pain.